Since 2010, when the brilliant Australian critic, poet and memoirist Clive James learned he had terminal leukemia, he’s had his afterburners flipped on. He has been on a vivifying late-career tear. During this time he’s released six books: poems, essay collections, even a warm and approachable full-dress translation of Dante’s “Divine Comedy.” At 76, the polymathic Mr. James is burning out, not fading away.

There isn’t yet a perfect anthology of Mr. James’s best work, although compilations like “As of This Writing: The Essential Essays, 1968-2002” are very good. A true “Portable Clive” would be an essential book, panoramic in scope. It would include excerpts from his memoirs and a dense lot of his poems. It would contain a great deal of his intellectual journalism for publications in England, where he has lived most of his adult life: television criticism, travel writing and prose about obsessions like Formula One racing and the tango as well as pronouncements on literary subjects. I’m not alone in scanning the horizon for it.

His new volume of poems, “Sentenced to Life,” feels like the most important of his late books. It’s a harrowing collection, gravid with meaning, unflinching in its appraisal of the author’s mistakes, including infidelity, and plain-spoken in its reckoning with his life’s terminus.

Many of this book’s 37 poems feel built to last, including “Lecons de tenebres” — lessons of darkness — in which Mr. James seems to speak not merely for himself but for so many who have allowed career and ego to fizz too freely at the front in their minds. This poem includes these lines:

The mirror holds the ruins of my face
Roughly together, thus reminding me
I should have played it straight in every case,
Not just when forced to. Far too casually
I broke faith when it suited me, and here
I am alone, and now the end is near.
All my life I put my labour first.
I made my mark, but left no time between
The things achieved, so, at my heedless worst,
With no life, there was nothing I could mean.

This poem ends with the poet sensing what “the years have brought/A fitting end, if not the one I sought.”

This would not be a Clive James book if it were not also replete with offbeat humor and flyaway cultural observations. In one poem, while in a hospital, he catches a Sylvester Stallone movie on television and comments, “No-one grits/Like Sly: it looks like a piano sneering.” Most of the keepers in “Sentenced to Life,” however, are the poems that wring meaning from addressing the time the poet has left. In “Event Horizon,” he writes:

What is it worth, then, this insane last phase
When everything about you goes downhill?
This much: you get to see the cosmos blaze
And feel its grandeur, even against your will,
As it reminds you, just by being there,
That it is here we live or else nowhere.

His other recent book is “Latest Readings,” a collection of essays in which the author revisits favorite books and takes the temperature of some new ones. “If you don’t know the exact moment when the lights will go out,” he tells us, “you might as well read until they do.”

Mr. James made a vow to himself, he remarks early on, that his book-buying days were over. He breaks this vow instantly, of course. Nearly every essay in this collection describes a haul from his favorite used bookstore in Cambridge, where he lives, or from the online seller AbeBooks.com. Purchasing books via his laptop makes him wonder “what life will be like when you will merely have to think of something you want and it will arrive instantly, still crackling with the ozone of the time-space continuum.” You’ll never be alone, with a Bezos drone.

Not all of these essays rank near Mr. James’s best work. Like Sinatra near the end, he’s become more of a belter, less willing to tease out a phrase or an idea. Some pieces are little more than reviews of his old reviews. I worry when he starts to reread not only favorite books but also favorite series. When he writes, “Yes, I must read the Hornblower books again soon,” you think: Surely there are better uses of your time, man!

Yet “Latest Readings” is a plain demonstration that Mr. James remains as learned and as funny as any critic on earth. His essay on the literature of Washington is a perfect example. Bob Woodward, he says, “checks his facts until they weep with boredom.”

He suggests that “Personal History,” the 1997 memoir by Mr. Woodward’s former boss, the Washington Post publisher Katharine Graham, is undervalued for class reasons. “I wonder why the book is not more often cited by feminists,” he says. “Perhaps too many of them are too far on the left, and don’t believe that a poor little rich girl can have real problems.”

The personal digressions in “Latest Readings” tend to be first rate. While denouncing hard drugs, Mr. James remarks: “At one period I was the kind of pothead who looked like a small cloud being propelled by a pair of legs.” He compares his imitation of the German soprano Elisabeth Schwarzkopf to another man’s, and writes that onstage Schwarzkopf “looked as if she were trying to kiss the behind of a hummingbird in midflight.”

At its end, “Latest Readings” tells how Mr. James wishes to be remembered. “If the young feel compelled to come and see your tomb, there should be something good written on it,” he writes. “Here in Cambridge, in Trinity College Chapel, there is a plaque dedicated to Ludwig Wittgenstein. It says, in Latin, that he released thought from its bonds in language. If I ever had a plaque, I would like it to say: He loved the written word, and told the young.”